FX vs DX for long shots

So i can use my D300 (DX body) with my 70-200 (FX lens) to replicate a longer focal length. (1.5 x 200 = 300mm). If i bought an FX body and used the same lens, it would be a 200mm focal length for real, but if i only used the 'center' of the image it would effectively be a 300mm image.

But what about the IQ?

The D300 has 12 million pixels. The new d300 (FX) has 24 million pixels, but in the example about, I'd only be using 'some' of them. IF i'm counting correctly, the DX sensor is about 43% the size of the D600 sensor (371 sq mm vs 862). If i use 42% of the larger sensor on this hypothetical image, that is 10.3 million pixels. So would I be correct to conclude that 10.3 million for the FX setup would be lower quality than the 12.3 million for that far away shot?

I realize for most of the work done using the full frame of both, there's no comparison.